Re: [Algorithms] Geodesic Sphere

[Dave E. <eb...@ma...>]

From: "Robert Dibley" <RD...@ac...>
> I don't think the geodesic is made of equilateral triangles ... in fact I
> believe the only solid of vaguely spherical shape that you can make with
> equilateral triangles is the icosahedron (20 tri's)

Yes.  The code I mentioned in an earlier post generates a
mesh of triangles that are not equilateral.  But a related
question might be the following.  Given a scalar function
that determines how 'close' a triangle is to equilateral, can
you construct a triangle mesh such that all its triangles
have metric smaller than a prescribed tolerance?  Such
a scalar function is F(T) = sum_{i=1}^3 |A_i - pi/3|^2 where
the A_i are the angles of the triangle T.  Or maybe a function
that is zero when all three sides have same length, positive
otherwise.  Or a combination of the two.

--
Dave Eberly
eb...@ma...
http://www.magic-software.com